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2023 BIMC keystage3-IWYMIC team Question 1

xIMC · 2023 BIMC keystage3-IWYMIC team

Question 1

The equation $x^3-9x^2+11x-1=0$ has the non-negative real roots $p$, $q$ and $r$. If $s=\sqrt p+\sqrt q+\sqrt r$, what is the value of $|s^4-18s^2-8s|$?